Water bottle cages are widely used by recreational bicyclists to carry water bottles with them when they ride. The most common type of cage in current use is made from aluminum bar stock by bending it into two generally U-shaped sections, between which the water bottle is nested. One of the U-shaped sections is welded to a bracket having holes for fasteners by which the cage is attached to the down tube or seat tube of the bicycle frame. The water bottles used with the cages have a circular cylindrical side wall, a bottom wall, a neck having a cap and a shoulder between the side wall and the neck. Water bottles of this type are marketed by several manufacturers, and while those from various suppliers are very similar, there are differences among them in the diameter of the side wall. Accordingly, not all water bottles fit into any given cage, so the purchaser has to make sure that the water bottle he or she buys will fit the cage or cages of his or her bicycle. Moreover, it is not uncommon for bicyclists riding in organized tours or some types of races to replace empty water bottles with full ones at points along the route, the full bottles being furnished at random from a supply. If the full water bottle does not fit conveniently or at all into the rider's cage, that rider has a bit of a problem. If the water bottle is too small, it is prone to bouncing out of the cage. If it is too large, it will be hard to remove it from the cage for use and return it to the cage, or it may even not be possible to put it into the cage at all.